Mumbai - August to October. This is the monsoon season and you would find heavy flooding at-least twice, which can hamper your traveling plans as you would be confined to your hotel.
Himachal Pradesh: December start : This is normally the tourist season there, but at-least one snow blizzard each season cuts off the entire state from outside.

Most of India would be unpleasant during the summer. In Delhi, in particular, the summer is the worst time to visit. The temperature goes above 40 degrees Celsius every year and usually gets to about 48. This is too hot to enjoy being outside, and you'll be need to go outside

I like the idea of this thread. It's different. From my own experience I can say that the worst time to visit Kerala is from May to June. It's too hot and rainy too. Same with Assam. I would never want to visit Tamil Nadu in May/June its so hot. I would do anything to avoid Kolkata in the summer too.

Worst time to visit Leh is after the monsoon season. Especially, if you're traveling via Manali. The rains bring with them landslides and the like. And the path is so remote that you wouldn't want to get stuck there.